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Steel and Composite Structures Volume 14, Number 1, January 2013 , pages 73-83 DOI: https://doi.org/10.12989/scs.2013.14.1.073 |
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On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams |
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Mahmoud Bayat, Iman Pakar and Mahdi Bayat
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| Abstract | ||
| In this paper Hamiltonian Approach (HA) have been used to analysis the nonlinear free vibration of Simply-Supported (S-S) and for the Clamped-Clamped (C-C) Euler-Bernoulli beams fixed at one end subjected to the axial loads. First we used Galerkin\'s method to obtain an ordinary differential equation from the governing nonlinear partial differential equation. The effect of different parameter such as variation of amplitude to the obtained on the non-linear frequency is considered. Comparison of HA with Runge-Kutta 4th leads to highly accurate solutions. It is predicted that Hamiltonian Approach can be applied easily for nonlinear problems in engineering. | ||
| Key Words | ||
| non-linear vibration, analytical solution, beam vibration, Runge-Kutta 4th | ||
| Address | ||
| Mahmoud Bayat, Iman Pakar and Mahdi Bayat: Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran | ||